IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS
文献类型：期刊论文
| 作者 | Fu, Yun-Shan; Dai, Yu-Hong
|
| 刊名 | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
 |
| 出版日期 | 2010-02-01 |
| 卷号 | 27期号:1页码:71-84 |
| 关键词 | Monotone projected gradient algorithm Support Vector Machine (SVM) adaptive steepest descent step-size Dai-Yuan step-size projection subproblem |
| ISSN号 | 0217-5959 |
| DOI | 10.1142/S0217595910002594 |
| 英文摘要 | In this paper, we consider the projected gradient algorithms for solving the quadratic program with bound constraints and a single linear equality constraint (SLBQP). We establish the relationship between the Lagrangian multiplier in the projection subproblem and the Lagrangian multiplier in the original optimization problem. Then we give an improved initial estimate of the Lagrangian multiplier in the subproblem based on this relationship. It appears that this initial estimate is very close to the optimal Lagrangian multiplier after several iterations of the outer loop. This will reduce at most 40% of the computing time in the projection subproblem. This initial guess can also be used in all kinds of projected gradient methods for solving the SLBQP problem. The numerical results show that it brings much more improvement in monotone algorithms than in nonmonotone algorithms. We also apply the adaptive steepest descent step-size and the Dai-Yuan step-size which are two monotone step-sizes to the projected gradient method of this SLBQP problem. Our numerical experiments showed that their performance can be better than some other monotone projected gradient methods. |
| 资助项目 | Chinese NSF[10571171] ; Chinese NSF[10831006] ; CAS[kjcx-yw-s7-03] |
| WOS研究方向 | Operations Research & Management Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000276687000006 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/11209]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Dai, Yu-Hong |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Fu, Yun-Shan,Dai, Yu-Hong. IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS[J]. ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH,2010,27(1):71-84. |
| APA | Fu, Yun-Shan,&Dai, Yu-Hong.(2010).IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS.ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH,27(1),71-84. |
| MLA | Fu, Yun-Shan,et al."IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS".ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 27.1(2010):71-84. |
入库方式： OAI收割
来源：数学与系统科学研究院
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